= Quadrupole strain scaling of a weak self-gravitating source
{title2=$E=O(\epsilon^2R/r),\quad\epsilon=GM/R$}
For a weakly self-gravitating bound source of size $R$, mass $M$ and nonspherical dynamical <mass quadrupole moment> $Q=O(MR^2)$, the <virial theorem> gives $v^2=O(GM/R)=O(\epsilon)$. Its time scale is $R/v$, so $\ddot Q=O(Mv^2)$. The <far-zone quadrupole strain> then has a spatial half-strain coefficient $E=O(GMv^2/r)=O(\epsilon^2R/r)$ in units $c=1$. The physical transverse-traceless strain is $2E^{\mathrm{TT}}$. Spherical or stationary sources can have zero radiation, so this is a characteristic scale for a changing nonspherical quadrupole, not a positive lower bound. The radiation zone also requires $r\gg R/v$.
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